CN103646166B - A kind of High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory - Google Patents

Abstract

The present invention relates to a kind of High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory, comprise: the FEM calculation of carrying out High temperature pipe of power station road system strength, the emphasis of determining High temperature pipe of power station road system detects position, apply the theoretical definite creep impairment parameter of non-probabilistic reliability, set up creep impairment probabilistic model by determining creep impairment parameter, lost efficacy according to creep impairment probabilistic model computation structure, according to detecting data, the material of High temperature pipe of power station road system and structural test result are set up the method for maintaining model based on fail-safe analysis, determine high temperature pipe system best maintenance time according to method for maintaining model and the actual cost of overhaul of engineering. adopt this kind of High temperature pipe of power station road system to realize non-probabilistic reliability method for maintaining, realize and efficiently and exactly determined structure probability reliability, can accurately determine maintenance program, can solve the method for maintaining of the high-temperature pipe phase class problem in other field, thereby the scope of application be comparatively extensive.

Description

A kind of High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory

Technical field

The present invention relates to a kind of High temperature pipe of power station road system maintenance method, especially relate to a kind of based on non-probabilistic reliabilityTheoretical High temperature pipe of power station road system maintenance method.

Background technology

The maintenance of High temperature pipe of power station road system is the major issue that firepower power station and heat energy factory pay close attention to, due to modern firepower electricityStand and heat energy factory in the general cost of high temperature and high pressure steam pipeline high, in addition due to material under high temperature and high pressure environment deteriorated because ofElement complexity be difficult to prediction, once High temperature pipe of power station road system easily breaks down. and break down will give enterprise economy withAnd social safety is brought tremendous influence.

In view of this, just seem very important for the maintenance of high-temperature pipe. In the sixties in last century, first the U.S. carriedGo out the method for maintaining based on reliability, set up comprehensive production maintenance and reliability in American and Britain, Deng developed country subsequentlyConcentrate the maintenance system combining. Develop into again later take into consideration the infringement that may cause after accident occurs etc. affect because ofElement set up based on Risk Monitoring technology. ASME " the gas line Integrity Management system of for example ASMESystem "; The oil gas that the Pas-petrol Pipeline Risk Assessment steering committee (PRASC) of seven group's compositions such as energy conduit association of Canada carries outPas-petrol Pipeline Risk Assessment research etc. is all used widely in engineering reality. From documents and materials, developed countriesCarry out a large amount of analytical works based on risk detection technique, accumulated a large amount of data.

In China, there is many-sided demand for the safety guarantee technology in High temperature pipe of power station road, the one, China is sent out just energeticallyExhibition supercritical generating technology, the raising of temperature and pressure has increased the operation risk of factory widely, and high-temperature pipe portion whereinThe service life of part does not also accumulate how many experiences at present; The 2nd, the main steam line of many power plant of China progresses into old-age groupPhase, generally reach 200,000 hours above (100,000 hours projected lives) running time, the longest accumulation active time nearly 400,000Hour; High-temperature and high-pressure technique is more and more applied in many high-tech sectors simultaneously, has also proposed new demand. AobviousSo, setting up a High temperature pipe of power station road method for maintaining based on Applications In Risk Technique that is suitable for China's national situation is very important.

If set up the method for maintaining based under Applications In Risk Technique of an applicable China's national situation, what must solve is importantProblem is:

(1) first due to China, to carry out this respect working time short, and the data of accumulation is few, how to utilize a small amount of effective informationSetting up Reliability Maintenance method and be one asks a question before very important.

(2) secondly, under the statistical distribution character that obtains different parameters, how can determine the random distribution of impairment parameterFunction is also a major issue.

(3) also have, draw method for maintaining model, according to the models coupling risk assessment of gained, obtain High temperature pipe of power station roadSystem best maintenance time of programme is also the important content that belongs to method for maintaining.

(4) be finally how to adopt modern method for maintaining to determine the problem of suitable method for maintaining, this problemThrough there being the technology of comparative maturity, do not do emphasis herein.

Summary of the invention

Technical problem to be solved by this invention, is just to provide one and only utilizes a small amount of information just can be pre-comparatively accuratelyTest tube road system reliability, can be efficiently and determine exactly structural reliability, accurately determine maintenance program, the scope of application comparativelyHigh temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory widely.

Solve the problems of the technologies described above, the technical solution used in the present invention is as follows:

A High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory, is characterized in that: comprise followingStep:

S1 carries out the FEM calculation of High temperature pipe of power station road system, selects the place of 1-5 place maximum stress, supervises as emphasisSurvey position;

S2 arranges fixation of sensor at keypoint part, adopts the method for infrared thermal imaging monitoring instrument complete detection system to adoptCollection obtains the detection data of high temperature pipe system;

S3, according to non-probabilistic reliability theory, determines the random parameter of the creep impairment of High temperature pipe of power station road system;

S4 sets up the creep impairment probabilistic model of High temperature pipe of power station road system; The structural failure of calculating high temperature pipe system is generalRate;

S5 is according to the creep damage failure probability of High temperature pipe of power station road system, computation structure fail result;

S6 is according to the detection data of the result of calculation of step (5), pipeline, material and structural test result, sets up based on canThe method for maintaining model of analyzing by property;

S7 is according to the method for maintaining models coupling risk assessment of gained, while obtaining the best maintenance of High temperature pipe of power station road systemBetween.

Described step S3 comprises following content:

According to the non-probabilistic model of following Formula creep impairment:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material constant; σ_eqFor etc. effectPower, and above-mentioned each parameter is stochastic variable;

To adopt the method in non-probabilistic reliability to define above-mentioned stochastic variable below:

First the minimum and maximum value of easily determining above-mentioned parameter according to engineering reality, therefore can obtain following intervalNumber: $[\underset{\_}{B},\stackrel{\_}{B}],[\underset{\_}{m},\stackrel{\_}{m}],[\underset{\_}{k},\stackrel{\_}{k}],[\underset{\_}{r},\stackrel{\_}{r}],[{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}},{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}];$

As follows according to the average of interval number defined parameters and standard deviation and the coefficient of variation:

$B_c=\frac{\stackrel{\_}{B}+\underset{\_}{B}}{2},B_D=\frac{\stackrel{\_}{B}-\underset{\_}{B}}{2},{\mathrm{cov}}_B=\frac{B_D}{B_c};$

$m_c=\frac{\stackrel{\_}{m}+\underset{\_}{m}}{2},m_D=\frac{\stackrel{\_}{m}-\underset{\_}{m}}{2},{\mathrm{cov}}_m=\frac{m_D}{m_c};$

$k_c=\frac{\stackrel{\_}{k}+\underset{\_}{k}}{2},k_D=\frac{\stackrel{\_}{k}-\underset{\_}{k}}{2},{\mathrm{cov}}_k=\frac{K_D}{k_c};$

$r_c=\frac{\stackrel{\_}{r}+\underset{\_}{r}}{2},r_D=\frac{\stackrel{\_}{r}-\underset{\_}{r}}{2},{\mathrm{cov}}_r=\frac{r_D}{r_c};$

${\mathrm{\σ}}_{\mathrm{eqc}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}+{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{\σ}}_{\mathrm{eqD}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}-{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{cov}}_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_{\mathrm{eqD}}}{{\mathrm{\σ}}_{\mathrm{eqc}}};$

It is B that definition above-mentioned parameter is respectively average_c,m_c,k_c,r_c,σ_eqc; Standard deviation is B_D,m_D,k_D,r_D,σ_eqD; The coefficient of variationCov_B,cov_m,cov_k,cov_r,cov_σRandom distribution, random distribution character is selected according to the principle of being partial to securityGet;

Described step S4 comprises following sub-step:

S4-1 selects the corresponding equivalent stress of regional of described High temperature pipe of power station road system as stratified samplingVariable;

If the equivalent stress σ that S4-2 is described_eqMeet following formula, this equivalent stress σ_eqCorresponding region is not forCan there is the region of creep damage failure:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

Wherein, B, D, k are stochastic variable, and:

Average+3 × the standard deviation of B=damage threshold value;

Average+3 × the standard deviation of k=damage threshold value;

Average-3 × the standard deviation of [D]=damage threshold value;

If the equivalent stress σ that S4-3 is described_eqMeet following formula, this equivalent stress σ_eqCorresponding region is for sending outThe region of raw creep damage failure:

${\mathrm{\σ}}_{\mathrm{eq}}>{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

S4-4 is occurring in the region of creep damage failure, utilize layered sampling method based on Monte Carlo method and by withLower formula calculates failure probability P_f：

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

Wherein, Num is test number (TN), and nf is the number of times losing efficacy in test, meets following relation:

The nonlinear degree that needs to reduce data in this method, is specially: data are taken the logarithm, thereby reduce the non-of dataLinear degree.

Described step 5 comprises the following steps:

First adopt the common Weibull of least square fitting, normal state and lognormal probability distribution function, therefromSelect the method for immediate probability-distribution function, set up the creep impairment probability mould of comparatively accurate High temperature pipe of power station road systemType;

According to following Formula creep impairment probabilistic model:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material parameter; σ_eqFor etc. effectPower, above-mentioned parameter is random parameter. Its random nature defines definite by non-probabilistic reliability interval number. And creep impairment value alsoIt is random parameter.

Calculate the structural failure probability of High temperature pipe of power station road system according to creep impairment probabilistic model and determine failure probability:

If described equivalent stress σ_eqMeet following formula, this equivalent stress σ_eqCorresponding region is not for sending outThe region of raw creep damage failure:

σ_eq≤[σ]_max；

Wherein, B, D, k are interval number, and [σ]_maxFor maximum in the interval function of following formula equal sign the right:

${\left[\mathrm{\σ}\right]}_{\max }={\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r}$

If described equivalent stress σ_eqMeet following formula, this equivalent stress σ_eqCorresponding region is for to wriggleThe region that loss on transmission wound lost efficacy:

σ_eq＞[σ]_max；

In order to obtain immediate creep impairment random distribution, will adopt equation of linear regression from normal state, lognormal andIn Weibull distribution, select the method for best distribution;

The step of Weibull Function of determining pipeline creep impairment is as follows:

Determine the cumulative risk function of prediction according to following formula

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i};$

Wherein, t_kFor failure event time of origin, n is the total number of times of generation event, wherein also comprises the thing that there is no inefficacyPart, the inefficacy moment of each product is t by ascending sequence₁≤t₂≤...≤t_n；

Determine based on Weibull probability distribution function in conjunction with the result of calculation of Larson-Miller method according to following formulaUnreliable degree function F (t):

F(t_rex/t_res)=1-exp{-(t_rex/t_resη)^m}；

Wherein, t_rex/t_resThe ratio in the life-span of calculating for test life and corresponding use Larson-Miller method formulaValue, m is form parameter, η is scale parameter; Brief note t=t_rex/t_res, its probability-distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)}；

Determine the regression equation of cumulative risk function according to following formula:

H(t)=(t/η)^m；

lnH(t)=mlnt-mlnη

Wherein, m, η are the determined parameter of equation of linear regression;

According to equation of linear regression y_i=a+bx_i, and determine the parameter of Weibull Function according to following formula:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\};$

Thereby set up corresponding Weibull probability life-span distribution function.

Described step S6 is specially:

According to following Formula periodic plan Maintenance Model:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C_TFor total maintenance cost in the unit interval; C_cFor the expense of each correction maintenance; C_pFor taking of preventive maintenanceWith; Or, according to following Formula preventive maintenance model:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C_TFor total maintenance cost in the unit interval; C_cFor the expense of each correction maintenance; C_pFor taking of preventive maintenanceWith.

Described step S7 comprises the following steps:

S7-1 determines the risk R (t) of High temperature pipe of power station road system according to following formula:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx};$

Wherein, R (t)=P_f(t)·C(t)，P_f(t) be the failure probability of structure, the consequence of C (t) for losing efficacy and producing, it is allIt is the function of time t; P_f(t) and C (t) separate, and R (t) is fuzzy random variable, f (x, t) is R (t) and P_f(t) takeFrom identical probability distribution, the identical membership function that m (x, t) has with C (t) for R (t), f (x, t) and m (x, t) are equalContinuously;

S7-2 utilizes linear programming algorithm to calculate the best dimension of described High temperature pipe of power station road system by following formulaRepair time t:

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right);$

Wherein,Represent function R (t) to obtain with linear programming algorithm the best maintenance time of high temperature pipe.

Beneficial effect: high-temperature pipe confucian orthodoxy method for maintaining of the present invention, owing to wherein having adopted non-probabilistic reliability theory, because ofThis can lack in adequate data amount situation, utilizes low volume data to determine parameters random distribution; And utilize two kinds to be applicable toThe MC method with high efficiency calculating of high temperature pipe creep impairment problem, and adopted the combination of Reliability Maintenance theoretical methodThe method for maintaining of the high-temperature pipe damage problem of risk assessment technology, thus only utilize a small amount of information just can be pre-comparatively accuratelyTest tube road Problem of System Reliability, has realized efficiently and has determined exactly structural reliability, determines maintenance program, its particularly suitableA series of implementation methods in enterprise in formulation high-temperature pipe structural reliability maintenanceization, and can solve in other fieldThe method for maintaining of high temperature pipe phase class problem, thus the scope of application is comparatively extensive.

Brief description of the drawings

Fig. 1 is the overall flow figure of High temperature pipe of power station of the present invention road system maintenance method;

Fig. 2 is High temperature pipe of power station of the present invention road system FEM model figure.

Detailed description of the invention

In order more clearly to understand technology contents of the present invention, describe in detail especially exemplified by following examples.

Refer to shown in Fig. 1, high temperature pipe system maintenance method of the present invention, comprises the following steps:

1, first carry out the FEM calculation of High temperature pipe of power station road system, according to the place of maximum stress, determine that power station is highThe emphasis of temperature pipe-line system detects position;

2, arrange fixation of sensor at keypoint part, adopt the method for infrared thermal imaging monitoring instrument complete detection system to adoptCollection detects data;

3, according to the theoretical creep impairment random parameter of determining High temperature pipe of power station road system of non-probabilistic reliability, comprise followingStep:

(a) according to obtained test, detection data minimum, maximum, according to interval number definition in non-probabilistic reliabilityMethod, determines average, standard deviation and the coefficient of variation of random parameter;

(b) according to inclined to one side principle of sound accounting, the probability distribution function of the relevant random parameter of definition;

Be specially:

According to the non-probabilistic model of following Formula creep impairment:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material constant; σ_eqFor etc. effectPower, and above-mentioned each parameter is stochastic variable;

Above-mentioned stochastic variable will adopt the method in non-probabilistic reliability theory to define:

First the minimum and maximum value of easily determining above-mentioned parameter according to engineering reality, obtains following interval number:

$[\underset{\_}{B},\stackrel{\_}{B}],[\underset{\_}{m},\stackrel{\_}{m}],[\underset{\_}{k},\stackrel{\_}{k}],[\underset{\_}{r},\stackrel{\_}{r}],[{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}},{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}];$

As follows according to the average of interval number defined parameters and standard deviation and the coefficient of variation:

$B_c=\frac{\stackrel{\_}{B}+\underset{\_}{B}}{2},B_D=\frac{\stackrel{\_}{B}-\underset{\_}{B}}{2},{\mathrm{cov}}_B=\frac{B_D}{B_c};$

$m_c=\frac{\stackrel{\_}{m}+\underset{\_}{m}}{2},m_D=\frac{\stackrel{\_}{m}-\underset{\_}{m}}{2},{\mathrm{cov}}_m=\frac{m_D}{m_c};$

$k_c=\frac{\stackrel{\_}{k}+\underset{\_}{k}}{2},k_D=\frac{\stackrel{\_}{k}-\underset{\_}{k}}{2},{\mathrm{cov}}_k=\frac{k_D}{k_c};$

$r_c=\frac{\stackrel{\_}{r}+\underset{\_}{r}}{2},r_D=\frac{\stackrel{\_}{r}-\underset{\_}{r}}{2},{\mathrm{cov}}_r=\frac{r_D}{r_c};$

${\mathrm{\σ}}_{\mathrm{eqc}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}+{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{\σ}}_{\mathrm{eqD}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}-{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{cov}}_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_{\mathrm{eqD}}}{{\mathrm{\σ}}_{\mathrm{eqc}}};$

It is B that definition above-mentioned parameter is respectively average_c,m_c,k_c,r_c,σ_eqc; Standard deviation is B_D,m_D,k_D,r_D,σ_eqD; The coefficient of variationCov_B,cov_m,cov_k,cov_r,cov_σRandom distribution, random distribution character is selected according to the principle of being partial to securityGet.

4, by determining the probability distribution of described creep impairment parameter, set up the creep impairment probability of high temperature pipe systemModel. The wherein probability distribution function of creep impairment, needs by more conventional Weibull, normal state and logarithm normal distributionRegression equation relatively obtain.

Due to regression equation existing definition in reliability theory of normal state and logarithm normal distribution, therefore repeat no more,Definition Weibull function comprises the following steps:

(a) determine the cumulative risk function of prediction according to following formula

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i};$

Wherein, t_kFor failure event time of origin, n is the total number of times of generation event, wherein also comprises the thing that there is no inefficacyPart,

The inefficacy moment of each product is t by ascending sequence₁≤t₂≤...≤t_n；

(b) determine based on Weibull probability and distribute in conjunction with the result of calculation of Larson-Miller method according to following formulaThe unreliable degree function F (t) of function:

F(t_rex/t_res)=1-exp{-}t_rex/t_resη)^m}；

Wherein, t_rex/t_resThe ratio in the life-span of calculating for test life and corresponding use Larson-Miller method formulaValue, m is form parameter, η is scale parameter; Brief note t=t_rex/t_res, its probability-distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)}；

(c) according to the regression equation of the definite cumulative risk function of following formula:

H(t)=(t/η)^m；

lnH(t)=mlnt-mlnη

Wherein, m, η are the determined parameter of equation of linear regression;

(d) according to equation of linear regression y_i=a+bx_i, and determine the parameter of Weibull Function according to following formula:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\};$

Thereby set up corresponding life expectance distribution function;

5, calculate the creep damage failure probability of High temperature pipe of power station road system according to described creep impairment probabilistic model, bagDraw together following steps:

(a) select the corresponding equivalent stress of regional of described High temperature pipe of power station road system to become as stratified samplingAmount;

(b) if described equivalent stress σ_eqMeet following formula, this equivalent stress σ_eqCorresponding region is not for canThere is the region of creep damage failure:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

Wherein, B, D, k are stochastic variable, and:

Average+3 × the standard deviation of B=damage threshold value;

Average+3 × the standard deviation of k=damage threshold value;

Average-3 × the standard deviation of [D]=damage threshold value;

(c) if described equivalent stress σ_eqMeet following formula, this equivalent stress σ_eqCorresponding region is for occurringThe region of creep damage failure:

${\mathrm{\σ}}_{\mathrm{eq}}>{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

(d) occurring in the region of creep damage failure, utilize layered sampling method based on Monte Carlo method and by withLower formula calculates failure probability P_f：

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

Wherein, Num is test number (TN), and nf is the number of times losing efficacy in test, meets following relation:

6, according to the material of described detection data, High temperature pipe of power station road system and structural test result and described knotStructure failure probability, sets up the method for maintaining model based on fail-safe analysis, is specially:

According to following Formula periodic plan Maintenance Model:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C_TFor total maintenance cost in the unit interval; C_cFor the expense of each correction maintenance; C_pFor taking of preventive maintenanceWith;

Or, according to following Formula preventive maintenance model:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C_TFor total maintenance cost in the unit interval; C_cFor the expense of each correction maintenance; C_pFor taking of preventive maintenanceWith;

7, determine the risk R (t) of High temperature pipe of power station road system according to following formula:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx};$

Wherein, R (t)=P_f(t)·C(t)，P_f(t) be the failure probability of structure, the consequence of C (t) for losing efficacy and producing, it is allIt is the function of time t; P_f(t) and C (t) separate, and R (t) is fuzzy random variable, f (x, t) is R (t) and P_f(t) takeFrom identical probability distribution, the identical membership function that m (x, t) has with C (t) for R (t),

F (x, t) and m (x, t) are all continuous;

8, utilize linear programming algorithm to calculate the best maintenance time of described high temperature pipe system by following formulat：

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right);$

Wherein,Represent function R (t) to adopt linear programming algorithm to obtain the best maintenance time of high temperature pipe.

In above formula, determine the factor and the structural failure probability P that affect high-temperature pipe structural life-time_f(t) method is as follows:

(1) determine the high-temperature pipe life-span is affected to large factor

For affecting the more feature of high temperature pipe factors of limit life, first to remove as far as possible high-temperature pipe was affected to the life-spanLittle factor, only leaves the factor that impact is large. In conventional fail-safe analysis, what usually adopt is parameters sensitivity analysis sideMethod, determines that in reliability model, impact is large namely to comparatively those parameters of sensitivity of result. But this method is notCan be effectively applied to analyze a large amount of hot test data.

Rough set (RoughSet) theory is a kind of ambiguous and mathematical tool uncertain problem of processing. In the methodThe reasoning of decision rule be widely used in medicine and pharmacology, business, finance, market survey, Engineering Control and design wide spectrum itIn. Rough set theory is a kind of very effective theory in Copyright Law About Databases excavates, and has obtained significant effect. AndHave and used the research report of distinguishing material character from material composition.

Therefore, first utilize rough set theory to determine the method for material impact parameter in test data. Concrete analysisStep is as follows:

(a) first will manage to reduce the nonlinearity in testing of materials data, the impacts such as enchancement factor, for example, according to ashCumulative or regressive method minimizing randomness in look theory; Can adopt for fatigue data the method that data are taken the logarithmTo reduce nonlinear degree.

(b) then experimental data after treatment is carried out to unified planning processing, so that analyze.

(c) data after treatment are calculated point according to the computational methods of information system decision table in rough set theoryAnalyse.

Step can be determined the sensitive parameter that affects material lifetime in test data effectively according to the above analysis.

(2) determine parameter probability distribution problem

After selecting the random parameter that influence factor is high, the problem that solve is how to confirm power station, chemical industry equipmentOr the probability-distribution function problem of the burn-out life of construction material.

This problem is one of sixty-four dollar question in design based on reliability and method for maintaining technical know-how. Generally trueThe failure probability function of fixed structure or member need to be by reliability test or by a large amount of numbers that comes from engineering realityAccording to determining. But because engineering actual environment or experimental condition are limit, sometimes can not obtain abundant data. CauseThis, can be according to relevant interval number define method in non-probabilistic reliability theory in conjunction with related reliability achievement in research, and it is fixed to be easy toAverage and the coefficient of variation and the distribution situation of the above-mentioned random parameter of justice.

In order to obtain the random distribution of pipeline creep comparatively accurately, the present invention adopts least square regression algorithm, passes throughThe method of the fitting result of more conventional Weibull, normal state and logarithm normal distribution, selects the probability of immediate realityDistribution function. Wherein determine Weibull distribution, the method proposing according to K.Fujiyama etc., step is as follows:

Suppose to have n product, each product failure moment by ascending sequence is

t₁≤t₂≤...≤t_n；

Determine the cumulative risk function (Estimatecumulativehazardfunction) of prediction with formula below:

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i}......\left(2.1\right)$

Wherein, t_kBe failure event time of origin, n is that the total number of times of generation event comprises the event that there is no inefficacy.

The data in fail data storehouse can be determined based on prestige cloth in conjunction with L-M method (Larson-Miller method) result of calculationThe unreliable degree function of your probability-distribution function, as follows

F(t_rex/t_res)=1-exp{-(t_rex/t_resη)^m}……（2.2）

Wherein, t_rex/t_resTest life and corresponding L-M method formula ratio mathematic(al) expectation. M is form parameter, and η is chiDegree parameter.

Brief note t=t_rex/t_res, its probability-distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)}……（2.3）

Obey in Weibull distribution situation at hypothesis failure probability function, for the regression equation of cumulative risk function asUnder:

H(t)=(t/η)^m……（2.4）

lnH(t)=mlnt-mlnη

Here, m, η are the determined parameters of equation of linear regression.

According to equation of linear regression:

y_i=a+bx_i

The parameter of Weibull Function is determined by following formula:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\}......\left(2.5\right)$

Adopt the processing method by formula (2.1)～(2.5), can be effectively according to high-temperature creep injury testing of materials dataFoundation becomes corresponding Weibull probability life-span distribution function. Because this life expectance distribution function both can be fixing at oneTime in express test data random distribution situation, can express again under time growth pattern, material creep damageLife expectance. Therefore profit can directly be determined the Probabilistic damage diagram of high temperature pipe in this way.

(3) accurate high efficiency computational methods

Property of probability in the high-temperature creep injury of metal material has obtained the testing of materials to be proved, researcher is logical conventionallyCross lot of experiments and determine on the basis of probability statistics character of associated materials parameter, set up some corresponding creep probability mouldsType. Usually adopt at present FOSM, the methods such as Monte Carlo are calculated creep damage failure probability.

Owing to not only only having normal distribution in the probability parameter of creep impairment and also having many kinds of Non-Gaussian Distribution, because ofThis adopts FOSM more difficult. And Monte Carlo method is because its method is easy, can be easily for containing notWith the analog simulation problem of dividing the probabilistic model that plants stochastic variable, in addition, because the method has integration dimension insensitiveAnd be easy to application feature. In engineering, be widely applied. But because its computational efficiency is lower, therefore for wrigglingLoss on transmission is hindered probabilistic model and is calculated above, particularly, for some complicated models, will spend many computing times. Therefore, howImproving computational efficiency is an important problem, and conventional method has selective sampling method and stratified sampling method at present. But these are two years oldKind method limitation is larger, therefore proposes to be applicable to high temperature pipe creep damage failure method for calculating probability below.

(3.1) Importance Sampling Method

Paper Importance Sampling Method, this method the most important thing is how to choose Importance Sampling Function, is to take separatelyA kind of distribution makes simulation have some to lay particular stress on (making creep damage failure increased frequency), and this being distributed in while sampling given prominence toPart to integral contribution maximum in integrand in formula, for fear of deviation is introduced to end product, finally will repairJust. Computing formula is as follows:

$P_f=\frac{1}{t}{\∫}_0^{t}h\left(a\right)\underset{i=1}{\overset{k}{\mathrm{\Π}}}\frac{f\left(a\right)}{f_i\left(a\right)}{f}_i\left(a\right)\mathrm{da}......\left(3.1\right)$

In formula: f (a) is the probability density function of former problem; f_i(a), (i=1 ..., be k) that the probability of selective sampling is closeDegree function.

Therefore the computing formula of selective sampling:

$P_f=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}h\left(a_i\right)\underset{i=1}{\overset{k}{\mathrm{\Π}}}\frac{f\left(a_i\right)}{f_j\left(a_i\right)}......(3.2)$

The selection principle of Importance Sampling Function is that can make has a large amount of observations in h (a) value interval. And f (x)/f₁(x) be compared to different x values, its fluctuation is not too large.

As can be seen from the above, select Importance Sampling Function will meet two conditions:

(1) can in h (a) value interval, there is a large amount of observations.

(2) reduce f (x)/f as far as possible₁(x) fluctuation of ratio under different x values.

From above-mentioned selection Importance Sampling Function principle, the method for choosing Importance Sampling Function is a lot. In order to facilitateSee, will adopt a kind of selective sampling using former probability density function to dangerous direction translation as creep impairment probability calculation belowThe method of function.

For creep impairment probability failure model:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k}......\left(3.3\right)$

T: expression time; B, m, k, r: be under fixed temperature by experiment determined material constant; σ_eq: equivalent stress.Above-mentioned parameter is stochastic variable.

According to the requirement of above-mentioned selection Importance Sampling Function, in this model, choose equivalent stress as selective sampling variable.By analysis and comparison, can determine the distance to a standard deviation of stress augment direction translation original function, important as thisThe average of sampling function, and variance is constant. Result of calculation shows, with the relative error of Monte Carlo direct sampling result of calculationBe less than in 10% situation, sampling number, by 10000 times of direct sampling Monte Carlo method, is reduced to importance Monte Carlo method and takes out1000 simulations of sample. That is to say 1/10 workload that only need to use direct sampling method.

(3.2) layered sampling method

Stratified sampling method is that another kind is usually used in improving sampling efficiency method, and its basic thought is to make integrated value tributeOffer large territorial sampling and more have more now, its Sampling Strategies is not change original probability distribution, but sampling interval is divided intoSome minizones, the number of sampling points in each minizone determines according to contribution, makes integrated value contribute large sampling moreHave more now, to improve sampling efficiency.

Consider integration:

$I=\underset{0}{\overset{l}{\∫}}f\left(x\right)\mathrm{dx}......\left(3.4\right)$

By an a for integrating range [0,1]_i(i=0,1,2 ..., m) being divided into m mutually disjoint subinterval, its length is dividedBe not:

l_i=a_i-a_i-1,(i=1,2,…,m;a₀=0,a_m=1)，

So

$I={\∫}_0^{l}f\left(x\right)\mathrm{dx}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\∫}_{a_{i-1}}^{a_i}f\left(x\right)\mathrm{dx}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{I}_i......\left(3.5\right)$

Ask each minizone [a by the mean value estimation technique_i-1，a_i] numerical integration value I_i(i=1,2 ..., m). If knownThe contribution of sampling to integration I in each minizone, road, just can determine frequency in sampling for its contribution, to those contributionsSample or unsample less in little region. Therefore just can reduce frequency in sampling, thereby improve sampling efficiency.

According to creep impairment probabilistic model (3.3), take above-mentioned relevant layered sampling method into consideration. Selection equivalent stress is doneFor stratified sampling variable, consider the different interval contribution differences to integration. Between some special section, for example stress value placeWhen Critical Damage value appears being greater than in the impairment value that interval calculates, can make this interval sample value needn't participate in calculating, directlyMaking its creep impairment value is 1. Otherwise some little stress are far not enough to make structure generation creep impairment to make creep impairment value be0. So just can effectively reduce frequency in sampling.

The formula that calculates failure probability value in the Monte Carlo method in each region is:

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

In formula: P_f: failure probability; Num: test number (TN). Nf: Failure count in experiment, its expression formula is as follows:

Can not occur the scope of creep impairment in order to determine stress, supposing is enough at other the numerical value of stochastic variableThe impairment value that makes creep impairment model is enough in large situation, and stress value still can not make impairment value be more than or equal to damage doorSill value.

Consider that stochastic variable value is as follows:

Average+3 × the standard deviation of B=damage threshold value

Average+3 × the standard deviation of k=damage threshold value

Average-3 × the standard deviation of [D]=damage threshold value

Can release according to above-mentioned formula, when below equivalent stress is less than when formula value, (in small probability situation) noCan there is the region of creep damage failure:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\};}^{1/r}$

Otherwise, can define equivalent stress (in large probability situation) and can make the region of structure generation creep rupture.

Can be calculated under different time by said method, equivalent stress can not exceed maximum (little) value of damage threshold.Therefore, just can the stratified sampling interval of reasonable arrangement to equivalent stress.

Last result of calculation shows, method in this paper can effectively reduce frequency in sampling. For example, in the time of t=400,Direct sampling method needs 10000 times, and stratified sampling method is with 4453 times.

(4) preventive maintenance and risk assessment

(4.1) preventive maintenance

In expense least model in maintenance cycle model, can adopt following two kinds of situations.

(a) periodic plan maintenance, the total maintenance cost in the unit interval is:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(4.1\right)$

In formula:

C_T: total maintenance cost in the unit interval; C_c: the expense of each correction maintenance; C_p: the expense of preventive maintenance.

(b) preventive maintenance:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(4.2\right)$

The wherein same above formula of parameter (4.1).

(4.2) risk analysis

High temperature pipe of power station road system reliability method for maintaining based on risk analysis is defined as follows,

R(t)=P_f(t)·C(t)

In above formula, R (t) represents risk; P_f(t) failure probability of expression structure; C (t) represent lost efficacy produce afterReally. They are all the functions of time t.

Known according to above discussion, the failure probability of structure can be determined by the method for probability statistics.

But because C (t) is the assessment about failure consequence, involve politics, economy, humanistic environment, enterprise development etc.Deng the impact of factors. Due to many analyses and the very difficult numeral that uses simply of discriminant criterion. Therefore this is notMay represent with probabilistic method merely. But the consequence producing due to structural failure, due to the restriction of objective condition,Therefore also can be considered as a kind of uncertain factor, i.e. fuzzy factors. So can adopt in fuzzy mathematics comprehensively pass judgment on, expertThe methods such as judge define this function.

At this moment risk R (t) is a problem that includes enchancement factor and these two kinds of uncertain factors of fuzzy factors. In vacationIf P_f(t) and in the separate situation of C (t). R (t) is an obedience and P_f(t) identical probability distribution f (x, t), with C(t) fuzzy random variable of identical membership function m (x, t).

Under the continuous condition of f (x, t), m (x, t), for a given time t, the calculation expression of risk is:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx}$

Above formula can adopt the integral algorithm of Fuzzy Reliability to solve.

But in the ordinary course of things, work as P_f(t) and C (t) be in the situation of known function, obtain based on risk assessmentBe to solve an optimization problem, best maintenance time

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right)$

Due to for different engineering problems, its C (t) difference, therefore will analyze as the case may be.

About above technical know-how knowledge, also can be with reference to Publication about Document:

(1) Zhang Xuhong. the Life Design of HTHP pipeline and the research of Predicting Technique. the master of Nanjing University of Technology opinionLiterary composition .2002;

(2) Tu Shandong. high temperature structural integrity principle. Science Press .2003:369～423;

(3) Zhao Jie etc., based on R6 containing defect pressure piping fracture failure risk analysis system system – theory and method (I). stoneOiling work institution of higher education, 2002(15) 4:50～53;

(4) Zhao Jie etc., based on R6 containing defect pressure piping fracture failure risk analysis system system – theory and method (II).Petrochemical industry institution of higher education, 2002(16) 5:61～64;

(5) Xie Yujun etc., containing the system – of defect pressure piping fracture failure risk analysis system based on PD6493 (I). petrochemical industryEquipment .2002 (31) 4:4～7;

As an example of the power station pipe-line system in certain company example, method of the present invention is described below:

The steam line of certain steam turbine is carried out to stress analysis. This part pipeline connects boiler, steam turbine and ignitron,Ignitron leads to steam turbine and the steam main main steam line (Φ 273 × 28, elbow radius R=1370mm) to ignitron,Main steam line is to connecting pipe and partial firing pipe (Φ 133 × 14.2, elbow radius R=600mm) and the part of ignitronFemale pipe (Φ 366.5 × 36, elbow radius R=1500mm).

Table 1 pipe design parameter and material parameter

1, high-temperature pipe structure creep Damage Analysis

First carry out finite element analysis, FEM model as shown in Figure 2. According to result of finite element, pipeline the highestStress does not exceed the applied stress of pipeline material at 540 DEG C, therefore can safe operation. The position part that wherein stress is higher withWhat design drawing provided matches in (place that needs to install creep monitoring point in design drawing), and the stress of pipe bent position is general in additionHigher, creep monitoring point should be separately set. Note: the stress at support point place is higher is mainly to simplify because analyze the load at medium-height trestle placeFor point load, what actual conditions will be good is many.

By the high-temerature creep result of the test of high-temperature pipe material 10CrMo910, can determine following creep impairment public affairs againFormula:

${\stackrel{\·}{\mathrm{\ϵ}}}_c=B{\mathrm{\σ}}^n......\left(6.1\right)$

With:

$\stackrel{\·}{D}=A{\left(\frac{\mathrm{\σ}}{1-D}\right)}^P......\left(6.2\right)$

In material parameter.

B:7.488×10^-22；n:8.3704；A:2.071×10^-19；p:7.27166；

σ: equivalent stress, determine according to FEM calculation. Wherein, the maximum stress of bend pipe is 35.2MPa.

And according to the calculating of structure creep stress, the equivalent stress of bend pipe is 28.16MPa.

2, the CALCULATION OF FAILURE PROBABILITY of high temperature pipe

In conjunction with reference to pertinent literature, can determine the distribution situation of stochastic variable according to above-mentioned analysis, order:

A obeys logarithm normal distribution, the coefficient of variation is 0.05;

P Normal Distribution, the coefficient of variation is 0.05;

σ Normal Distribution, the coefficient of variation is 0.1;

D_crLimit impairment parameter Normal Distribution, average is 0.417, the coefficient of variation is 0.1.

Adopt Monte Carlo direct sampling method to calculate (computational methods are shown in that Part II is described above), frequency in sampling is 10⁷Inferior. Result of calculation is in table 2.

The failure probability of table 2 bend pipe creep impairment

Year	Failure probability	Year	Failure probability
				1	6.000e-7	9	1.406e-4
2	2.700e-6	10	1.804e-4
				3	7.700e-6	11	2.299e-4

4	1.560e-5	12	2.780e-4
				5	2.830e-5	13	3.390e-4
6	4.830e-5	14	4.037e-4
				7	7.390e-5	15	4.790e-4
8	1.080e-4

For serviceability method for maintaining computing formula more easily, above-mentioned result of calculation is brought into young waiter in a wineshop or an innIn the equation of linear regression of multiplication (concrete grammar sees above face portion), can obtain in Weibull, normal state and logarithm normal distributionUnder fitting parameter.

Table 3 bend pipe calculated data Fitted probability distributed constant result

Distribution property	Distributed constant	Coefficient correlation
			Weibull distribution	M＝2.5288，η＝3.0639e2	0.9994
Normal distribution	μ＝43.3091，σ＝9.2063	0.9583
			Logarithm normal distribution	μ’＝8.2860，σ’＝1.6755	0.9974

3, Reliability Maintenance method is calculated

In upper table 6.3, with the coefficient correlation maximum in the fitting result of Weibull distribution, fitting effect is best. According toThe feature that Weibull Distribution data are good, and often adopt in engineering. Therefore, adopt Weibull distribution as this hereStructure creep impairment Reliability Function,

$R\left(t\right)=\exp (-{\left(\frac{t}{\mathrm{\η}}\right)}^m)......\left(6.3\right)$

In the expense least model in maintenance cycle model, be divided into two kinds of situations.

(1) periodic plan maintenance, the total maintenance cost in the unit interval is:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(6.4\right)$

In formula,

C_T: total maintenance cost in the unit interval; C_c: the expense of each correction maintenance; C_p: the expense of preventive maintenance.

(2) preventive maintenance:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(6.5\right)$

The wherein same above formula of parameter (6.4).

Due to correction maintenance and the unknown of preventive maintenance expense, suppose preventive maintenance expense C below_pBe a unit, respectivelyConsider correction maintenance expense and preventive maintenance expense ratio, C_c/C_pIn=6,11,16 situation, the total maintenance cost calculating.

After work 100000 hours, failure probability is 1.804e-4. Use above-mentioned two kinds of methods to calculate, the results are shown in Table 4.

Table 4 is in total maintenance cost of 100,000 hours back elbows of work

Cc/Cp	Periodic plan maintenance	Preventive maintenance
			1	0.08761	0.08761
6	0.08764	0.08771
			11	0.08767	0.08782
16	0.08797	0.08793

In above-mentioned calculating, all consider the maintenance of pipeline after breaking down and there is no the preventative dimension under a situation arisesRepair situation. But being installed, sensor carries out after real time on-line monitoring, and can be keeping in repair again after breaking down in the pastExpense, reduces and becomes the expense that preventative maintenance will spend.

Namely realize at C_c/C_p=1 o'clock, repair. Can be seen by table 4, maintenance cost is all kinds of maintenance costsWith in minimum.

Equally, according to result of finite element with about the calculating of creep stress, the equivalent stress that obtains straight tube is 22MPa,Its coefficient of variation is 0.1. Other parameter is the same, and calculation procedure is identical. The work that finally obtains is after 100000 hours, failure probabilityFor 4.2e-7. Maintenance cost sees the following form.

Table 5 is in total maintenance cost of work straight tube after 100,000 hours

Cc/Cp	Periodic plan maintenance	Preventive maintenance
			1	0.0876002	0.0876002
6	0.0876003	0.0876005
			11	0.0876004	0.0876009
16	0.0876005	0.0876012

4, based on the definite method for maintaining of risk assessment technology

After the related data obtaining by on-the-spot online detection instrument, then by finite element analysis and above-mentioned method for maintaining meterAfter calculation and Analysis. Can calculate in certain time period, pipeline has the failure probability value of two place's fault locations. For example there is individual lacking at straight tube placeFall into position 1, have individual defect 2 in pipe bent position. Can calculate the failure probability value at corresponding site place according to related data.

Defect 1 place, failure probability value is 1.2 × 10^-6；

Defect 2 places, failure probability value is 1.0 × 10^-6。

While using FEM calculation again, find that stress concentration phenomenon occurs at this place.

Characterizing method according to risk:

R=P_f·C

In formula, R is value-at-risk; P_fIt is failure probability; C is the consequence that failure event occurs.

Consider the consequence causing due to inefficacy below, will mainly consider (1) economic loss; (2) cause material at this positionDamage; (3) impact that corrosion causes.

Consider this pipe fitting economic loss factor causing that lost efficacy, give points 10 points, be divided into unacceptable loss (10～6.5), heavy losses (6.4～3.5) and can accept loss (3.4～0) three standards.

Material is caused to damage, need to consider whether inside configuration has stress to concentrate and wait energy accelerating structure Failure Factors existingResemble. Be divided into equally Three Estate, major injury (10～6.5), general damage (6.4～3.5), can ignore damage (3.4～0).

Corrosion condition is divided into three grades, seriously corroded (10～6.5), and general corrosion (6.4～3.5), slight corrosion (3.4～0)。

Definition failure consequence is evaluated as:

C=C₁·C₂·C₃

First the damage at pipeline position is evaluated:

Table 6 straight tube position parameters data

C1Economic loss	C2Material damage	C3Corrosion condition	C
				5	3	1	15

The damage at bend pipe position is evaluated, and consider in calculating with finite element simulation and find that there is region of stress concentration,And by detecting this defect of finding just on region of stress concentration, due to special shape and this pipe fitting outside of bend pipeEnvironment, finds that corrosion condition is serious. Therefore evaluate situation as follows.

Table 7 bend pipe position parameters data

C1Economic loss	C2Material damage	C3Corrosion condition	C
				5	10	8	400

Last risk assessment is:

Pipeline place defect: R=P_f·C=1.2×10^-6×30=3.6×10^-5

Pipe bent position defect risk assessment:

R=P_f·C=10^-6×400=4×10^-4

Consider that such Pipeline Failure form mostly shows as toughness and tears inefficacy. According to risk assessment table 6.8, machinery knotStructure can be converted into minimax risk criterion failure probability, as shown in the table.

Table 8 frame for movement SI recommendation tables

RELIABILITY INDEX	3.71	4.26	4.75
				Probable range	10-4	10-5	10-6
Failure consequence	Not serious	Seriously	Very serious

Because pipeline failure consequence is not serious, therefore can use failure probability 10^-4, as the standard of needing repairing. According to upperThe result of calculation of stating, the risk assessment of pipe bent position defect is above standard, therefore needs to keep in repair immediately.

From above institute's discussion method and example, the method applied in the present invention, can detect judgement effectively, in real timeThe situation of high-temperature pipe, determines whether to need repairing, and therefore can extend round of visits.

Adopt the method for above-mentioned High temperature pipe of power station road system maintenance method, owing to wherein having adopted in non-probability theoryDetermine the method for random parameter, therefore can for lack in mass data situation, utilize low volume data determine parameters withMachine distribution property, and utilize two kinds of MC methods that high efficiency is calculated that have that are applicable to high-temperature pipe creep impairment problem, andAdopt the method for maintaining of Reliability Maintenance theoretical method in conjunction with the high-temperature pipe damage problem of risk assessment technology, thus only sharpJust can predict comparatively accurately pipe-line system integrity problem by a small amount of information, realized efficiently and determined that exactly structure canBy property, accurately determine maintenance program, it is specially adapted to enterprise and is formulating a series of of high temperature pipe structural reliability maintenanceizationImplementation method, and can solve the method for maintaining of the high temperature pipe phase class problem in other field, thus the scope of application is comparativelyExtensively.

Claims (4)

1. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory, is characterized in that: comprise followingStep:

S1 carries out the FEM calculation of High temperature pipe of power station road system, according to the place of maximum stress, determines emphasis monitoring position;

S2 arranges fixation of sensor at keypoint part, the inspection that adopts the collection of infrared thermal imaging monitoring instrument to obtain high temperature pipe systemSurvey data;

S3, according to non-probabilistic reliability theory, determines the random parameter of the creep impairment of High temperature pipe of power station road system;

S4 sets up the creep impairment probabilistic model of High temperature pipe of power station road system, calculates the structural failure probability of high temperature pipe system;

S5 is according to the creep damage failure probability of High temperature pipe of power station road system, computation structure fail result;

S6, according to the detection data of the result of calculation of step (5), pipeline, material and structural test result, sets up based on reliabilityThe method for maintaining model of analyzing;

S7 is according to the method for maintaining models coupling risk assessment of gained, obtains High temperature pipe of power station road system best maintenance time;

Described step S3 comprises following content:

According to the non-probabilistic model of following Formula creep impairment:

$\stackrel{.}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material constant; σ_eqFor equivalent stress, andAbove-mentioned each parameter is stochastic variable;

Above-mentioned stochastic variable will adopt the method in non-probabilistic reliability theory to define:

First the minimum and maximum value of easily determining above-mentioned parameter according to engineering reality, obtains following interval number:

$[\underset{\‾}{B},\stackrel{\‾}{B}],[\underset{\‾}{m},\stackrel{\‾}{m}],[\underset{\‾}{k},\stackrel{\‾}{k}],[\underset{\‾}{r},\stackrel{\‾}{r}],[{\underset{\‾}{\mathrm{\σ}}}_{\mathrm{eq}},{\stackrel{\‾}{\mathrm{\σ}}}_{\mathrm{eq}}];$

As follows according to the average of interval number defined parameters and standard deviation and the coefficient of variation:

$B_c=\frac{\stackrel{\‾}{B}+\underset{\‾}{B}}{2},B_D=\frac{\stackrel{\‾}{B}-\underset{\‾}{B}}{2},{\mathrm{cov}}_B=\frac{B_D}{B_c};$

$m_c=\frac{\stackrel{\‾}{m}+\underset{\‾}{m}}{2},m_D=\frac{\stackrel{\‾}{m}-\underset{\‾}{m}}{2},{\mathrm{cov}}_m=\frac{m_D}{m_c};$

$k_c=\frac{\stackrel{\‾}{k}+\underset{\‾}{k}}{2},k_D=\frac{\stackrel{\‾}{k}-\underset{\‾}{k}}{2},{\mathrm{cov}}_k=\frac{k_D}{k_c};$

$r_c=\frac{\stackrel{\‾}{r}+\underset{\‾}{r}}{2},r_D=\frac{\stackrel{\‾}{r}-\underset{\‾}{r}}{2},{\mathrm{cov}}_r=\frac{r_D}{r_c};$

${\mathrm{\σ}}_{\mathrm{eqc}}=\frac{{\stackrel{\‾}{\mathrm{\σ}}}_{\mathrm{eq}}+{\underset{\‾}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{\σ}}_{\mathrm{eqD}}=\frac{{\stackrel{\‾}{\mathrm{\σ}}}_{\mathrm{eq}}-{\underset{\‾}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{cov}}_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_{\mathrm{eqD}}}{{\mathrm{\σ}}_{\mathrm{eqc}}};$

It is B that definition above-mentioned parameter is respectively average_c,m_c,k_c,r_c,σ_eqc; Standard deviation is B_D,m_D,k_D,r_D,σ_eqD; The coefficient of variation iscov_B,cov_m,cov_k,cov_r,cov_σRandom distribution, random distribution character is chosen according to the principle of being partial to security;

Described step S4 comprises following sub-step:

S4-1 selects the corresponding equivalent stress of regional of described High temperature pipe of power station road system as stratified sampling variable;

If the equivalent stress σ that S4-2 is described_eqMeet following formula, this equivalent stress σ_eqCorresponding region is not for occurringThe region of creep damage failure:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

Wherein, B, D, k are stochastic variable, and:

Average+3 × the standard deviation of B=damage threshold value;

Average+3 × the standard deviation of k=damage threshold value;

Average-3 × the standard deviation of [D]=damage threshold value;

If the equivalent stress σ that S4-3 is described_eqMeet following formula, this equivalent stress σ_eqFor there is creep in corresponding regionThe region that damage was lost efficacy:

${\mathrm{\σ}}_{\mathrm{eq}}>{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

S4-4, occurring in the region of creep damage failure, utilizes layered sampling method based on Monte Carlo method and by following publicFormula is calculated failure probability P_f：

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

Wherein, Num is test number (TN), and nf is the number of times losing efficacy in test, meets following relation:

The nonlinear degree that reduces data adopts the data mode of taking the logarithm.

2. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, its spyLevy and be: described step 5 comprises the following steps:

First adopt the common Weibull of least square fitting, normal state and lognormal probability distribution function, therefrom selectThe method of immediate probability-distribution function, sets up the creep impairment probabilistic model of High temperature pipe of power station road system comparatively accurately;

According to following Formula creep impairment probabilistic model:

$\stackrel{.}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material parameter; σ_eqFor equivalent stress, onState parameter and be random parameter. Its random nature defines definite by non-probabilistic reliability interval number. And creep impairment value be also withMachine parameter.

Calculate the structural failure probability of High temperature pipe of power station road system according to creep impairment probabilistic model and determine failure probability:

If described equivalent stress σ_eqMeet following formula, this equivalent stress σ_eqFor not there is creep in corresponding regionThe region that damage was lost efficacy:

σ_eq≤[σ]_max；

Wherein, B, D, k are interval number, and [σ]_maxFor maximum in the interval function of following formula equal sign the right:

${\left[\mathrm{\σ}\right]}_{\max }={\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r}$

If described equivalent stress σ_eqMeet following formula, this equivalent stress σ_eqFor there is creep impairment in corresponding regionThe region of losing efficacy:

σ_eq＞[σ]_max；

In order to obtain immediate creep impairment random distribution, will adopt equation of linear regression from normal state, lognormal and Wei BuYou select the method for best distribution in distributing;

The Weibull distribution method of wherein determining pipeline creep impairment comprises the following steps:

Determine the cumulative risk function of prediction according to following formula

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i};$

Wherein, t_kFor failure event time of origin, n is the total number of times of generation event, wherein also comprises the event that there is no inefficacy, everyThe inefficacy moment of individual product is t by ascending sequence₁≤t₂≤…≤t_n；

Determine based on Weibull probability distribution function not in conjunction with the result of calculation of Larson-Miller method according to following formulaReliability Function F (t):

F(t_rex/t_res)＝1-exp{-(t_rex/t_resη)^m}；

Wherein, t_rex/t_resFor test life and the ratio in the life-span that uses accordingly Larson-Miller method formula to calculate, mFor form parameter, η is scale parameter; Brief note t=t_rex/t_res, its probability-distribution function is designated as:

F(t)＝1-R(t)＝1-exp{-H(t)}；

Determine the regression equation of cumulative risk function according to following formula:

H(t)＝(t/η)^m；

lnH(t)＝mlnt-mlnη

Wherein, m, η are the determined parameter of equation of linear regression;

According to equation of linear regression y_i＝a+bx_i, and determine the parameter of Weibull Function according to following formula:

m＝b

$\mathrm{\η}=\exp \{-\frac{a}{m}\};$

Thereby set up corresponding Weibull probability life-span distribution function.

3. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, its spyLevy and be: described step S6 is specially:

According to following Formula periodic plan Maintenance Model:

$C_T=\frac{C_p}{T_p}+C_c\frac{{\∫}_0^{T_p}(1-R\left(t\right))\mathrm{dt}}{T_p{\∫}_0^{T_p}R\left(t\right)\mathrm{dt}};$

Wherein, C_TFor total maintenance cost in the unit interval; C_cFor the expense of each correction maintenance; C_pFor the expense of preventive maintenance;

Or, according to following Formula preventive maintenance model:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_p}R\left(t\right)\mathrm{dt}}+C_p\frac{R\left(T_p\right)}{{\∫}_0^{T_p}R\left(t\right)\mathrm{dt}};$

Wherein, C_TFor total maintenance cost in the unit interval; C_cFor the expense of each correction maintenance; C_pFor the expense of preventive maintenance.

4. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, its spyLevy and be: described step S7 comprises following sub-step:

S7-1 determines the risk R (t) of High temperature pipe of power station road system according to following formula:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx};$

Wherein, R (t)=P_f(t)·C(t)，P_f(t) be the failure probability of structure, the consequence of C (t) for losing efficacy and producing, it is allThe function of time t; P_f(t) and C (t) separate, and R (t) is fuzzy random variable, f (x, t) is R (t) and P_f(t) obeyIdentical probability distribution, the identical membership function that m (x, t) has with C (t) for R (t), f (x, t) and m (x, t) all connectContinuous;

When S7-2 utilizes linear programming algorithm to calculate the best maintenance of described High temperature pipe of power station road system by following formulaBetween t:

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right);$

Wherein,Represent function R (t) to obtain with linear programming algorithm the best maintenance time of high temperature pipe.